This invention relates generally to a system and method for filtering a signal and in particular to a system and method for filtering a digital signal and changing its sampling rate from a first rate to a second different rate which is a process known as resampling.
When an analog signal, such as music or the like, is converted into a digital signal, it is sampled at some predetermined rate known as the sampling rate. The sampling rate can vary, but it is typically set at a particular value for a particular application. The sampling rate used for a particular application typically depends on the Nyquist theorem. The Nyquist theorem states that if you have a signal with a bandwidth of A kHz, then you need (2Axc3x971000) samples so that data is not lost in the conversion from analog to digital. For example, a voice signal may be sampled at 8 kHz, CD quality music (which has a bandwidth from 0 kHz to 20 kHz) may be sampled at 44.1 kHz and a digital audio tape may be sampled at 48 kHz. A typical high quality FM signal may be sampled at 32 kHz.
In many applications, it is desirable to have the output sample rate be different from the input sample rate. The process of altering the data sample rate is called xe2x80x9cresamplingxe2x80x9d. For example, a person may listen to a CD with music on it that is typically sampled at 44.1 kHz and then want to play the song as high quality FM signals which requires the digital data to be resampled from 44.1 kHz to 32 kHz.
The algorithm that performs this resampling process is called a xe2x80x9cmultirate filterxe2x80x9d and is a process by which a mathematical equation is applied to the original signal in order to generate the new sample rate signal. Multirate filters are used for resampling but also for anti-aliasing. There are many different ways of implementing the multirate filter. With the classical tapped-delay-line FIR filter design approach, the multirate filter implementation usually results in a very long filter length. Consequently, the implementation is expensive and has an undesirably long filter delay. Most of the time it is unrealistic to realize a multirate filter with this approach because it is too expensive and too slow.
For a resampling operation in which one is converting between a first integer value and a second integer value that are mathematically related to each other by an integer, the resampling process is relatively straight-forward. For example, to convert between 4000 samples per second and 8000 samples per second, a 2:1 filter is used that doubles the sampling rate. However, for a resampling operation in which the two different sampling rates are not related to each other by an integer value (e.g., 2), the resampling process is much more complex and can be handled in one or more different manners.
First, the resampling from an initial lower sampling rate to a higher final sampling rate can be completed by up converting the initial sampling rate to an integer value that is higher than the final sampling rate, but is a least common multiplier of both the initial sampling rate and the final sampling rate. Then, the up converted signal is down converted back to the desired final sampling rate. For example, to convert from a 44.1 kHz CD signal to a 48 kHz DAT signal, the signal is first upconverted by an integer value (e.g., 160) to a first value (7056 kHz) and then down converted by another integer value (e.g., 147) to the desired 48 kHz sampling rate. The problem is that the typical tapped delay-line filter for this resampling has as many as 3000 delays so that the resampling process is very slow and computationally expensive.
One technique to accomplish this is a multirate filter that can be realized by using a cascade of several simple multirate subfilters as is well known. Each subfilter performs a segment of the resampling process. As an example, an 18:1 multirate filter can be realized by two 3:1 multirate filter followed by a 2:1 multirate filter. The cascade filter approach is often selected to lower the total computational burden of the resampling and to lower the required data storage. However for small integer resampling, the benefits of cascade filters are small and the overhead of operating separate subfilters may overcome the small gains.
The other approach is to partition the multirate filter into collection of subfilters to generate a well known polyphase filter. With the polyphase filter, the subset of filter coefficients needed to compute a given output point are those that intersect the nonzero data points in the span of the filter""s total impulse response. With this approach the computation are effectively reduced since the total delay associated with the polyphase filter is much less than the typical cascade filter. However, a large number of subfilters are needed to achieve a specified distortion requirement.
Another conventional technique is to interpolate the polyphase filter results. For example, one can compute the approximation to the desired output by interpolation using the following equation:
y(m)=(1xe2x88x92xcex1m)y1(m)+xcex1my2(m) 
However, this technique is still to computationally intensive for many applications. Thus, it is desirable to provide a filter system that overcomes the above limitations and problems with resampling and it is to this end that the present invention is directed.
The resampling system and apparatus in accordance with the invention achieves and provides a cost-effective and computationally efficient resampling process. In the preferred embodiment, the resampling process achieves the resampling from a 44.1 kHz digitally sampled signal on a CD into a 32.kHz digitally sampled signal that may be stored digitally in a memory of a portable music device or stored in some other persistent storage medium. To achieve the computationally efficient resampling, the filter system may use a predetermined range of sub-filters (e.g., 22-24 in the preferred embodiment) in a polyphase filter so that the typical interpolation that is typically necessary for a polyphase filter is avoided. In more detail, the number of sub-filters is chosen such that a nearest neighbor strategy is used in which, for each sample point, the sample point is assigned to its closest neighbor which eliminates the interpolation and reduces the computation by a factor of two without sacrificing the output quality of the output resampled signal.
Thus, in accordance with the invention, a computer implemented resampling filter is provided. The resampling filter has a polyphase filter having between 20 and 25 sub-filter elements so that a desired output sample is adjacent to a sample from the sub-filter elements, and a nearest neighbor determiner for selecting whether a desired output sample from the resampled signal is assigned to a first resampled sample or to a second resampled signal.
In accordance with another aspect of the invention, a resampling filter for converting from a 44100 samples per second signal to a 32000 samples per second signal is provided having similar elements. In accordance with another aspect of the invention, a computer implemented resampling method comprises selecting a desired sample, y(m) according to the following equations
y(m)=y2(m) if xcex1mxe2x89xa71xe2x88x92xcex5 or 
y(m)=y1(m) if xcex1m less than xcex5
wherein y1(m) is a first sample, y2(m) is a second sample, xcex1m=(I)(tm), xcex5 is the error, I is the number of filters in the polyphase filter and tm is the time that the first sample lags the desired sample.